Phys. Rev. E 60, 6172–6175 (1999)Efficient algorithm for detecting unstable periodic orbits in chaotic systemsReceived 8 March 1999; revised 2 June 1999; published in the issue dated November 1999 We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of an iterative scheme and an effective technique for selecting initial points. The iterative scheme is based on the semi-implicit Euler method, which has both fast and global convergence, and only a small number of initial points is sufficient to detect all unstable periodic orbits of a given period. The power of our method is illustrated by numerical examples of both two- and four-dimensional maps. © 1999 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.60.6172
DOI:
10.1103/PhysRevE.60.6172
PACS:
05.45.-a
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